In [1]} the authors have shown that in the category of logarithmic schemes (and stacks), there is a unique minimal model of the universal logarithmic Jacobian that is not representable by an algebraic stack. The study of this so-called universal logarithmic Picard variety \(\operatorname{\mathcal {L}og\mathcal {P}ic}_{g,n,d}\)  can be traced back to Illusie [2]} and has subsequently received attention in [3]}, [4]}, [5]}, [6]}. The authors of [1]} also introduce the universal tropical Picard variety, which universally over \(\mathcal {M}_{g,n}^{log}\)  is denoted by \(\operatorname{\mathcal {T}ro\mathcal {P}ic}_{g,n,d}\) . It parametrizes tropical curves together with a torsor over the sheaf of harmonic or linear functions on \(\Gamma \)  of degree \(d\)  and it naturally arises as the tropicalization of \(\operatorname{\mathcal {L}og\mathcal {P}ic}_{g,n,d}\)  via a natural tropicalization morphism \(\operatorname{\mathcal {L}og\mathcal {P}ic}_{g,n,d}\rightarrow \operatorname{\mathcal {T}ro\mathcal {P}ic}_{g,n,d}\) .
